It's worth noting that Russia (then USSR) was the one that introduced the Latin alphabet in 1927 in the first place. Before that, it was Arabic. So, arguably, if they wanted to fully reverse the effects of imperialism, no matter the cost, they should go for Arabic.
From a practical standpoint, though, Arabic doesn't make sense - it's more complicated to learn, vastly more different from the alphabets of all neighboring languages (starting with the whole right-to-left thing), and most other Turkic languages use Latin-based alphabets these days.
But if the choice of Latin is dictated by pragmatic considerations, then it's reasonable to compare it to Cyrillic on the same grounds.
The original attempts to latinize (replacing Arabic) writing systems in those republics were, in fact, carried out by USSR, and it was very much a top-down thing, not some local initiative. USSR had a massive country-wide latinization campaign in 1920s for basically all languages spoken anywhere in the country that didn't already use Cyrillic. Long-term plans were to latinize everything, including Russian itself (this one went as far as a final proposal by a committee in 1930).
It makes perfect sense when you realize that Soviet government, at that point, viewed itself as a first comer in a blaze of worldwide communist revolutions, that would ultimately produce a single worldwide federated communist state. Per Marxist dogma about industrial workers being the vanguard of the revolution, the expectation was that the center of gravity would shift to Western Europe once revolutions happened there. Communist utopias of that time period generally assumed that such unification would result in adoption of some common language, and that Latin script would be used for that language. So adopting Latin for Soviet languages made sense in preparation.
When Stalin abandoned the concept of "world revolution", and switched instead to "socialism in one country", with a heavy dose of Russian nationalism underpinning the new ideology, all this was scrapped, and (then already established) Latin writing systems were replaced with Cyrillic ones, from roughly mid 1930s onward. Those Cyrillic writing systems are the ones inherited by the Asian republics at the dissolution of the USSR.
Still seems rather anachronistic and stupid, to say the least. When India became independent, there was a similar nativist drive: you can see how many of the major cities were renamed and such. Luckily people realized there was no real benefit to get rid of the English based education that was already in place. Something which I am personally immensely thankful for.
From a practical standpoint, though, Arabic doesn't make sense - it's more complicated to learn, vastly more different from the alphabets of all neighboring languages (starting with the whole right-to-left thing), and most other Turkic languages use Latin-based alphabets these days.
But if the choice of Latin is dictated by pragmatic considerations, then it's reasonable to compare it to Cyrillic on the same grounds.